To solve the equation \(\frac{2}{9} x - 4 = \frac{2}{3}\), we need to isolate the variable \(x\). First, add 4 to both sides of the equation to eliminate the constant term on the left side. Then, multiply both sides by the reciprocal of \(\frac{2}{9}\) to solve for \(x\).
To solve the equation \(\frac{2}{9}x - 4 = \frac{2}{3}\), we first isolate the term containing \(x\) by adding 4 to both sides of the equation:
\[
\frac{2}{9}x - 4 + 4 = \frac{2}{3} + 4
\]
This simplifies to:
\[
\frac{2}{9}x = \frac{2}{3} + 4
\]
Next, we simplify the right side of the equation:
\[
\frac{2}{3} + 4 = \frac{2}{3} + \frac{12}{3} = \frac{14}{3}
\]
So the equation becomes:
\[
\frac{2}{9}x = \frac{14}{3}
\]
To solve for \(x\), multiply both sides by the reciprocal of \(\frac{2}{9}\), which is \(\frac{9}{2}\):
\[
x = \frac{14}{3} \times \frac{9}{2}
\]
Simplifying the right side:
\[
x = \frac{14 \times 9}{3 \times 2} = \frac{126}{6} = 21
\]
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